On Fixed Point Results in Neutrosophic Metric Spaces Using Auxiliary Functions - Anwar Bataihah; Ayman. A Hazaymeh (Neutrosophic Sets and Systems)
In this paper, we establish novel fixed point theorems in the framework of neutrosophic metric spaces (NMS) by introducing the concept of neutrosophic (L, φ)-contractions. These contractions generalize classical contractive conditions by incorporating a function L that bounds the interaction between displacement terms and a control function φ that modulates the contraction intensity. Under specific hypothesis, we prove that every neutrosophic (L, φ)-contraction on a complete NMS admits a unique fixed point. As applications, we derive several corollaries by specifying the forms of L and φ, including cases where L is linear, additive, or defined via maximum functions. Our results unify and extend existing fixed point theorems in neutrosophic settings, while illustrative examples demonstrate their practical applicability.